Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes

Oluwafemi Stephen Ojambati, Allard Mosk, Ivo Micha Vellekoop, Aart Lagendijk, Willem L. Vos

Research output: Contribution to journalArticleAcademic

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Abstract

We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.
Original languageEnglish
Pages (from-to)-
Number of pages18
JournalarXiv.org
Publication statusSubmitted - 11 Feb 2016

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wave scattering
density distribution
flux density
eigenvectors
spatial distribution
energy conversion
S matrix theory
internal energy
illuminating
solar cells
waveguides
solid state
thresholds
scattering
lasers

Keywords

  • IR-100776
  • METIS-317341

Cite this

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title = "Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes",
abstract = "We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2{\%}. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.",
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Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes. / Ojambati, Oluwafemi Stephen; Mosk, Allard; Vellekoop, Ivo Micha; Lagendijk, Aart; Vos, Willem L.

In: arXiv.org, 11.02.2016, p. -.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - Energy density distribution of shaped waves inside scattering media mapped onto a complete set of diffusion modes

AU - Ojambati, Oluwafemi Stephen

AU - Mosk, Allard

AU - Vellekoop, Ivo Micha

AU - Lagendijk, Aart

AU - Vos, Willem L.

N1 - Open access

PY - 2016/2/11

Y1 - 2016/2/11

N2 - We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

AB - We show that the spatial distribution of the energy density of optimally shaped waves inside a scattering medium can be described by considering only a few of the lowest eigenfunctions of the diffusion equation. Taking into account only the fundamental eigenfunction, the total internal energy inside the sample is underestimated by only 2%. The spatial distribution of the shaped energy density is very similar to the fundamental eigenfunction, up to a cosine distance of about 0.01. We obtained the energy density inside a quasi-1D disordered waveguide by numerical calculation of the joined scattering matrix. Computing the transmission-averaged energy density over all transmission channels yields the ensemble averaged energy density of shaped waves. From the averaged energy density obtained, we reconstruct its spatial distribution using the eigenfunctions of the diffusion equation. The results from our study have exciting applications in controlled biomedical imaging, efficient light harvesting in solar cells, enhanced energy conversion in solid-state lighting, and low threshold random lasers.

KW - IR-100776

KW - METIS-317341

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